Methods and systems for employing dynamic risk-based scheduling to optimize and integrate production with a supply chain

ABSTRACT

A production and inventory control for a manufacturing facility is provided that facilitates and coordinates improved planning and execution of such facility in a supply chain with a focus on providing an improved and robust planning, production and inventory control, even in the presence of uncertainty. This may include Optimal Planning that can balance the need for low inventory, low cost (i.e., high utilization of equipment and labor), and efficient on-time delivery. The result of such planning is not a schedule per se but a set of parameters that form a dynamic policy that generates an evolving schedule as conditions (demand, production) materialize. An Optimal Execution applies the dynamic policy resulting in a manufacturing system that is robust enough to accommodate moderate changes in demand and/or capacity without the need to reschedule. Optimal Execution may also involve a “Capacity Trigger” that detects when the assumptions regarding demand and capacity used to determine the dynamic policy are no longer valid. The Capacity Trigger also may provide a Trigger Signal to the planner indicating the need for either more or less capacity.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.60/819,012 entitled, “METHOD FOR EMPLOYING DYNAMIC RISK-BASED SCHEDULINGTO OPTIMIZE AND INTEGRATE PRODUCTION WITH A SUPPLY CHAIN,” filed Jul. 7,2006, the disclosure of which is incorporated by reference herein in itsentirety.

BACKGROUND OF THE INVENTION

1.0 Field of the Invention

The invention relates generally to production and inventory control of amanufacturing facility or network of facilities and, more specifically,to a system and method that facilitates and coordinates improvedplanning and execution of such facilities in a supply chain with a focuson an improved planning, production and inventory control that is robustand effective, even in the presence of uncertainty.

2.0 Related Art

In recent years, companies have begun to appreciate the severity of therisks facing an entire corporation by not addressing potential supplychain problems. Indeed, more than two thirds of the companies surveyedby Accenture in 2006 said it had experienced a supply chain disruptionfrom which it took more than one week to recover. Furthermore, the studyrevealed that 73% of the executives surveyed had a major disruption inthe past 5 years. Of those, 36% took more than one month to recover. Onereason for this maybe that supply chains are (1) not designed with riskin mind and (2) are not robust enough to operate under conditionssignificantly different from those for which they are planned.

For many years, people have sought to develop processes that willgenerate optimal plans and schedules for managing production systems andtheir supply chains. The goal has been to reduce inventory, improvecustomer service, and to reduce cost by increasing the utilization ofexpensive equipment and labor. Unfortunately, these processes have notexplicitly considered risk and have ignored key facts regarding thesystems they try to control.

The first attempts in this area date back to the 1960's beginning withMaterial Requirements Planning (MRP) that provided material plans withno consideration of capacity. This evolved into Manufacturing ResourcesPlanning (MRP II), which provided some capacity checking modules aroundthe basic MRP functionality and, eventually, into the EnterpriseResources Planning (ERP) systems used today.

In the remainder of this application, any production planning systemwill be referred to as an ERP system whether it carries that moniker ornot. These can include so-called “legacy” systems that may employ onlybasic functionality such as MRP. Likewise, any system that is used todirectly control execution, whether it is part of an ERP system or not,will be referred to as a “Manufacturing Execution System” (MES).

Interestingly, virtually all ERP systems today (including the high endofferings of SAP and Oracle) provide MRP functions and continue to havethe same basic MRP calculations as the core of their production planningoffering. Not surprisingly, a 2006 survey showed that users gave lowmarks to these high end ERP/SCM systems for performance in distributionand manufacturing (averaging 2.5 and 2.6, respectively, out of 4.0). Ina survey performed by Microsoft of mid-sized companies (median revenueof $21 million, average around $100 million) 27% of 229 companies foundtheir ERP/SCM system to be “ineffective” and 46% found it to be only“somewhat effective.” Only 3% found the system used to be “veryeffective.”

There are two basic problems with these systems: (1) order sizing isdone without consideration of capacity and (2) planning lead times areassumed to be attributes of the part (see the book, Hopp and Spearman,Factory Physics, Foundations of Manufacturing Management, McGraw-Hill,New York, 2000, Chapter 5 for a complete discussion). The first issueresults in conservative (i.e., large) order sizes which increaseinventory and reduce responsiveness. The second issue is similar.Because the planning lead time does not depend on currentwork-in-process (WIP) levels and because being late (resulting in poorcustomer service) is worse than being early (resulting in extrainventory), most systems employ pessimistic (i.e., long) lead times. Theresult, again, is more inventory and less responsiveness and isespecially aggravated when the bill of material is deep.

Efforts to address these problems have gone on for many years but thebasic problems remain today. Consequently, most companies do not runtheir plants using the output of their ERP/SCM systems but, instead,“massage” the output using ad hoc spreadsheets.

Obviously, with this kind of “work around” there exists an opportunityto sell more sophisticated software and for some time now there havebeen numerous offerings known variously as “Advanced Planning andScheduling” or “Advanced Planning and Optimization.” These “APO”applications typically work between the Enterprise Resources Planning(ERP) system and the Manufacturing Execution System (MES). Although atypical ERP system contains many functions other functions, thisapplication focuses on those concerned with supply chain management suchas demand forecasting, customer order tracking, supplier management,inventory tracking, capacity planning, master production scheduling,material requirements planning, and the management of product dataincluding bills of material and routings. The MES is where the plansfrom the ERP are realized within the manufacturing facility andtypically includes functions such as work in process (WIP) tracking,shop order dispatching, product costing, and equipment tracking.

The APO is a more recent development that attempts to remedy some of theaforementioned problems found in ERP. However, APO's are in the form ofsome type of deterministic simulation of the process that assume thedemand, inventory, work in process, run rates, setup times, etc. are allknown which then seek to generate a schedule that is “optimal” undersome specified criteria. FIG. 1 presents an exemplary supply chain thatincludes a fabrication operation whose output is used in an assemblyoperation as well as a distribution function. FIG. 2 presents acomputational APO application operating with an ERP system and an MES.FIG. 3 illustrates the interrelations between these computationalfunctions.

One of the earliest APO's to appear that was moderately successful iscalled “Factory Planner®” and has been offered by i2 Corporation undervarious names (e.g., Rhythm®) since 1988. Offerings by Oracle® and SAP®in relatively recent products are different only in style and, perhaps,in the level of integration with other data.

Moreover, there are at least three problems that prevent the use ofdeterministic simulation as being an effective supply chain planning andscheduling tool:

1. The supply chain and plant have inherent randomness that do not allowfor the complete specification of a time for each shop order at eachprocess center with given labor component. Such detailed schedules areoften quickly out of date because of the intrinsic variability in thesystem. Moreover they do not manage risk which involves random eventsthat may or may not happen. In the past, this has been addressed usingever more detailed models requiring ever more computer power. Thismisses the point. Variability and risk are facts of life and are theresult of not only process variation (something that one attempts tocontrol) but also unforeseen events and variability in demand (thingsthat cannot be controlled). At any rate, the result is the sameregardless of the variability source. Detailed scheduling can onlyprovide a very short term solution and, in practice, the solution oftenbecomes invalid between the time it is generated and the time that theschedule is distributed and reviewed as part of production planningmeetings.

2. The detailed scheduling system must be re-run often because of theshort term nature of the solution. This becomes cumbersome and timeconsuming. Moreover, without a method for determining whether asignificant change has occurred, oftentimes the schedule is regeneratedin response to random noise (e.g., a temporary lull in demand) which isthen fed back into the system. Unfortunately, feeding back random noiseresults in an increase in the variability in the system beingcontrolled. Because of these problems, many companies have turned offtheir Advanced Planning and Scheduling systems after spending a greatdeal of money to install them.

3. It is essentially impossible to find an optimal schedule. Theproblems addressed are mathematically characterized as “NP-hard,” whichmeans that no algorithm exists that works in “polynomial” time to solvescheduling problems. The practical result is that for realistic problemsfaced in modern factories and in the supply chain, there is not enoughtime to find an optimal schedule regardless of the speed of thecomputer. Consequently, heuristics must be applied to generate a,hopefully, near optimal schedule. The effectiveness of these heuristicsis typically unknown for a broad range of applications.

These problems often result in a great deal of computer power being usedto create a detailed schedule for a single instance that will neverhappen (i.e., the random “sample path” will never be what is predicted apriori) and that becomes obsolete as soon as something unanticipatedoccurs.

The most advanced systems today offer two methods of planning formanufacturing supply chains: (1) “what-if” analysis using adeterministic simulation of the supply chain and (2) “optimization” of aset of “penalties” (again, using a deterministic simulation) associatedwith inventory, on-time delivery, setups, and wasted capacity. There arealso some crude methods for setting safety stock levels.

In addition to the fundamental problems listed above there are at twopractical problems with this approach: (1) what-if analysis is tediousand (2) optimizing a penalty function is not intuitive.

The tediousness of what-if analysis comes from all the detail that mustbe considered. FIG. 4 shows the output of a typical APO prior artapplication for the scheduled production on six machines in one factoryalong with projected inventory plot of one of the items produced,discussed more below. The planner can move shop orders in the scheduleand drill down on other items to view inventory projections. While thislevel of integration is impressive, it is not particularly usefulespecially when there are hundreds of machines (not to mention labor) toconsider along with thousands of individual items, each with their owndemand.

Likewise, the use of “penalties” to determine an “optimal” schedule isnot intuitive. What should the penalty be for carrying additionalinventory? What is the cost of a late order? What is the savingsgenerated by reducing the number of setups, particularly if there is noreduction in head count? What is the cost of having idle machines?

FIG. 1 is a block diagram of a typical prior art supply chain thatincludes a fabrication operation whose output is used in an assemblyoperation as well as a distribution function. The important concept hereis that the entire supply chain is comprised of only two types ofcomponents: stocks and flows.

Referring to FIG. 1, a simplified supply chain 1 includes Fabrication 2,Assembly 3, and Distribution 4. A plurality of raw materials come from asupplier 10 and are maintained in a Stock 11 until released into theproduct Flow 12 that may be embodied by one or more productionprocesses. Once completed the product is either shipped immediately 14(if the due date is passed) or is kept in a Stock 13 until the ship date(for make-to-order items) or until a demand occurs (for make-to-stockitems). In this typical scenario some parts are shipped to an Assemblyoperation 3 and others directly to a Distribution center 4. In thisexample, the Assembly process brings together a plurality of parts fromsuppliers and fabrication, performs an assembly operation as well asother processes, and then either maintains an inventory in a Stock orships to a Distribution site. The Distribution center comprising a Stock15 and a kitting and shipping process 16 whereby the parts are shippedto satisfy Market Demand 17.

FIG. 2 is a block diagram of a typical prior art approach to supplychain management using an ERP system 50, an MES 54, and an APO system52. Data for the ERP system is maintained in a data base 51 and includesall product information such as routings and bills of material as wellas information regarding equipment and labor capacity along with demandinformation. Using data from the ERP system, the planner generates aplan for the period 53 which may be a week or more. The plan is thenused to generate shop orders in the ERP system which is then executedusing the Manufacturing Execution System 54, 58 and put into production55. The MES also tracks WIP, cost, dispatch (i.e., prioritize) shoporders, track defects, etc. There may be scanners and sensors 56 thatautomatically collect data for WIP moving through the factory. There mayalso be computer monitors on the shop floor to indicate the status ofthe system 57.

FIG. 3 is a flow chart of a typical prior art approach to supply chainmanagement using an ERP system. Long-term planning including thegeneration of a long term forecast 66, the capacity resource planning70, together determine an aggregate production plan 68. Short-termplanning brings in make-to-order (MTO) and make-to-stock (MTS) demands72 as these occur into a Master Production Schedule 74. The planner mayuse the APO 88 to check capacity and due date feasibility of theschedule. Once a Master Production Schedule 74 is determined, MaterialRequirements Planning (MRP) 76 is used to generate demand for low levelcomponents. MRP data regarding the products and the system 84 includesbills of material to “explode” requirements for components based on theend product demand, inventory status data to determine net demand, lotsizing rules to determine the size of the shop orders, and planned leadtimes to determine when to launch purchase orders and shop orders. Onceall of the demand for all of the components has been generated, netted,and lot sized, a pool of purchase orders and shop orders is generated asplanned orders 78. The planner using the APO 88 then releases the shoporders at 80 to ensure on-time delivery and minimum inventory. This istypically done no more frequently than once per week. The Manufacturer'sExecution System MES 86 tracks the shop orders as they go throughproduction and provides information to the APO. These are releasedaccording to their release date if there is no APO. Alternatively, whenan APO is present, it is used to determine an “optimal” release datethat attempts to balance the conflicting desires of maintaining highutilization of resources while keeping inventories and cycle times low.

FIG. 4 is a representation of a prior art exemplary graphical userinterface (GUI) 90 for an APO providing schedule and inventoryinformation. This exemplary GUI presets a schedule for six machines 92and numerous parts. One part 94 is highlighted and a plot of projectedinventory is presented in the lower section of the GUI 96.

Accordingly, there is a need for an improved supply chain planning andscheduling tool that avoids one or more of the above drawbacks andlimitations of the prior art.

SUMMARY OF THE INVENTION

The invention provides a systems and methods to generate effectiveschedules that minimize required inventory while providing acceptable ontime delivery at the lowest possible cost (i.e., highest utilization ofmachines and labor). The systems and methods of the invention considerinherent randomness to be robust enough to accommodate moderate changesin demand and capacity without the need to reschedule.

The invention may be implemented in a number of ways. According to oneaspect of the invention, a computer-implemented method for trackingproduction in a given product flow against demand associated with aplurality of orders in the flow is provided. The method includes thesteps of determining a probability of shortage for the demand associatedwith at least one of the plurality of orders, determining expectedinventory-days for at least one of the plurality of orders in the flow,and generating output showing the probability of shortage associatedwith at least one of the plurality of orders and the expectedinventory-days for the at least one of the plurality of orders.

In another aspect, a computer-implemented method to signal insufficientor overabundance of capacity for a given flow operating under a givendemand is provided. The method includes the steps of determining thetotal expected inventory-days and overall probability of shortage for aspecified trigger, detecting when insufficient capacity is present andgenerating a first electronic signal based on the specified trigger,detecting when an overabundance of capacity is present and generating asecond electronic signal based on the specified trigger, and alteringcapacity in a production process according to the first or secondelectronic signal.

In another aspect, a system for tracking production in a given productflow against demand associated with a plurality of orders in the flow isprovided. The system includes means for determining a probabilitydistribution of finish times for all orders in the flow, means fordetermining a probability distribution of associated demand time for atleast one of the plurality of orders in the flow, means for determiningthe probability of shortage for the at least one associated demand basedat least in part on both probability distributions, and means fordisplaying a graph showing the overall probability of shortage for theat least one associated demand versus a specified parameter.

In yet another aspect, a computer program product comprising a computerusable medium having readable program code embodied in the medium isprovided. The computer program product includes at least one componentto cause or perform execution of the following steps: determining aprobability of shortage for the demand associated with each of theplurality of orders, determining expected inventory-days for each of theplurality of orders in the flow, and generating output showing theprobability of shortage associated with at least one of the plurality oforders and the expected inventory-days for the at least one of theplurality of orders.

In an additional aspect, a system for applying a dynamic policy to aproduction control system is provided. The system includes a dynamicrisk-based scheduling (DRS) system interoperably communicable with atleast one of an enterprise resources planning (ERP) system, amanufacturing execution system (MES), and a generic manufacturing database, wherein the DRS system includes: a optimal planning module thatgenerates a dynamic policy comprising parameters for balancing inventorylevels, utilization of equipment and labor, and on-time delivery, andthe parameters used for generating an evolving schedule as changes indemand and production capacity arise, and an execution module thatapplies the dynamic policy to accommodate changes in demand or capacitywithout rescheduling.

Additional features, advantages, and embodiments of the invention may beset forth or apparent from consideration of the following detaileddescription, drawings, and claims. Moreover, it is to be understood thatboth the foregoing summary of the invention and the following detaileddescription are exemplary and intended to provide further explanationwithout limiting the scope of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention, are incorporated in and constitute apart of this specification, illustrate embodiments of the invention andtogether with the detailed description serve to explain the principlesof the invention. No attempt is made to show structural details of theinvention in more detail than may be necessary for a fundamentalunderstanding of the invention and the various ways in which it may bepracticed. In the drawings:

FIG. 1 is a block diagram of a typical prior art supply chain thatincludes a fabrication operation whose output is used in an assemblyoperation as well as a distribution function.

FIG. 2 is a block diagram of a typical prior art approach to supplychain management using an ERP system, an MES, and an APO system;

FIG. 3 is a block diagram of a typical prior art approach to supplychain management using an ERP system;

FIG. 4 is a representation of a prior art graphical user interface (GUI)of an Advanced Planning and Optimization system (APO);

FIG. 5 is a flow chart of a typical prior art approach to supply chainmanagement using an ERP system equipped with an APO;

FIG. 6 is a functional flow diagram incorporating principles of theinvention, showing detail of single Flow and single Stock that make up alarger supply chain;

FIG. 7 is a block diagram illustrating an exemplary dynamic risk basedscheduling (DRS) system in which the functionality of the invention mayoperate;

FIG. 8 is a block diagram illustrating the relationship of DRSoperations in conjunction with an existing MES and ERP system, inaccordance with principles of the invention;

FIG. 9 is a block diagram of a DRS based system operating with planningand execution systems and showing several advantages over existingsupply chain management systems, according to principles of theinvention;

FIG. 10 is a flow diagram of an embodiment of a system of the inventioninvolving an ERP system;

FIG. 11 is a flow diagram of an embodiment of DRS used for planning andexecution independently of an ERP system, according to principles of theinvention;

FIGS. 12A and 12B are flow diagrams of an embodiment of the DynamicPolicy and CONWIP, according to principles of the invention;

FIG. 13 is a flow diagram of an embodiment of the Demand/ProductionTracking (DPT) module of FIG. 10, according to principles of theinvention;

FIG. 14 is a flow diagram describing an embodiment of the OptimizationModule, according to principles of the invention;

FIG. 15 is an equation showing the relation between demand (D), OOP cost(V), setup time (S), item cost (c), inventory carrying cost ratio (h)and ROQ (Q) and the LaGrange multipliers (λ), according to principles ofthe invention;

FIG. 16 is a flow diagram showing steps of an embodiment that may beused to determine an initial set of optimal re-order quantities,according to principles of the invention;

FIG. 17 is a representation of an exemplary graphical user interface(GUI) of the invention providing output and through which a user mayinput policy parameters and interact with the optimal Planning Module;

FIG. 18 is a representation of an exemplary graphical user interface(GUI) of the invention providing output showing the results after theoptimization, according to principles of the invention;

FIG. 19 is a representation of an exemplary graphical user interface(GUI) providing output showing the LaGrange multipliers for machinecapacity, according to principles of the invention;

FIG. 20 is a flow diagram of steps of an embodiment used in the Planningmodule to determine optimal CONWIP levels for a flow, according toprinciples of the invention;

FIG. 21 is a graph showing the output of an embodiment of the optimalCONWIP level estimation tool, according to principles of the invention;

FIG. 22 is a representation of a graphical user interface (GUI) of theinvention showing the output of an embodiment of the CONWIP Sequenceexecution process;

FIG. 23A is a representation of a graphical user interface (GUI) of theinvention showing the output of an embodiment of the Production/DemandTracking with a Capacity Trigger;

FIG. 23B is a pie chart output showing how much overtime is used, inaccordance with FIG. 23A;

FIG. 24A is a representation of an exemplary graphical user interface(GUI) of the invention showing the output of an embodiment of theProduction/Demand Tracking with a Capacity Trigger; and

FIG. 24B is a pie chart reflecting overtime usage in accordance with theoutput of FIG. 24A.

DETAILED DESCRIPTION OF THE INVENTION

The embodiments of the invention and the various features andadvantageous details thereof are explained more fully with reference tothe non-limiting embodiments and examples that are described and/orillustrated in the accompanying drawings and detailed in the followingdescription. It should be noted that the features illustrated in thedrawings are not necessarily drawn to scale, and features of oneembodiment may be employed with other embodiments as the skilled artisanwould recognize, even if not explicitly stated herein. Descriptions ofwell-known components and processing techniques may be omitted so as tonot unnecessarily obscure the embodiments of the invention. The examplesused herein are intended merely to facilitate an understanding of waysin which the invention may be practiced and to further enable those ofskill in the art to practice the embodiments of the invention.Accordingly, the examples and embodiments herein should not be construedas limiting the scope of the invention, which is defined solely by theappended claims and applicable law. Moreover, it is noted that likereference numerals represent similar parts throughout the several viewsof the drawings.

It is understood that the invention is not limited to the particularmethodology, protocols, devices, apparatus, materials, applications,etc., described herein, as these may vary. It is also to be understoodthat the terminology used herein is used for the purpose of describingparticular embodiments only, and is not intended to limit the scope ofthe invention. It must be noted that as used herein and in the appendedclaims, the singular forms “a,” “an,” and “the” include plural referenceunless the context clearly dictates otherwise.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meanings as commonly understood by one of ordinary skillin the art to which this invention belongs. Preferred methods, devices,and materials are described, although any methods and materials similaror equivalent to those described herein can be used in the practice ortesting of the invention.

The invention generally provides systems and methods for:

-   -   1. Optimal Planning that can balance the need for low inventory,        low cost (i.e., high utilization of equipment and labor), and        efficient on-time delivery. The result of such planning is not a        schedule per se but a set of parameters that form a dynamic        policy that generates an evolving schedule as conditions        (demand, production) materialize.    -   2. Optimal Execution that applies the dynamic policy resulting        in a manufacturing system that is robust enough to accommodate        moderate changes in demand and/or capacity without the need to        reschedule. Optimal Execution also involves the embodiment of a        “Capacity Trigger” that detects when the assumptions regarding        demand and capacity used to determine the dynamic policy are no        longer valid. The Capacity Trigger provides a Trigger Signal to        the planner indicating the need for either more or less        capacity.        The Optimal Planning method of the invention may feature a        method to optimize parameters used in commonly available        Enterprise Resource Planning (ERP) systems (e.g., MRP        parameters) and then use the optimized ERP system to generate        the dynamic policy. A different embodiment would replace the        production planning features of the ERP with features to        generate the dynamic policy within the invention.

ERP parameters for optimization may include but are not limited toavailable machine and labor capacity, order quantities, maximum WIPlevels, safety stocks, and planning lead times. In accordance with thisinventive method, the optimal dynamic policy is determined that canrespond to moderate changes in demand and capacity without the need toreschedule.

In one embodiment, a method seeks to determine a dynamic policy thatminimizes total inventory in a Flow-Stock combination 100 (i.e., bothWIP and finished stocks) subject to an established constraint foron-time delivery as well as constraints on capacity and the orderquantities (e.g., minimum, maximum, and incremental constraints). Inanother embodiment, in addition to the above considerations, certain“out-of-pocket” expenses are considered that are associated with a setup(or changeover from one product to another).

Examples of out-of-pocket costs include material lost during achangeover and destruction of certain jigs and fixtures needed tofacilitate the changeover, etc. Since the principles of the inventionseek to provide an optimal policy for a given set of machine and laborcapacities, time used by these resources is not considered an“out-of-pocket” expense. In an additional embodiment, in addition to allof the above considerations, raw material inventory carrying cost isincluded. Those skilled in the art will recognize that it is possible toinclude more and more elements of the supply chain until they are allconsidered, if desired.

The invention also provides a system and a computer program implementingthe described methods herein, as well as output via a computer screen,file, or a printer.

Other aspects of the invention provide for optimal execution using theaforementioned dynamic policy. These aspects include (but are notlimited to) one or more of the following:

-   -   1. A re-order point, re-order quantity (ROP,ROQ) system for        make-to-stock items.    -   2. Generation of shop orders (including order sizing, and        planned lead times (PLT)) for make-to-order demand.    -   3. A CONstant Work In Process (CONWIP) release methodology used        for both make-to-stock and make-to-order items. As those skilled        in the art would recognize, CONWIP is a generalized “pull”        method that is useful to prevent “WIP explosions” and excessive        cycle times.    -   4. A technique to sequence as opposed to schedule the shop        orders. Sequencing specifies only the order of the shop orders        to be maintained through the flow and, therefore, requires much        less information than scheduling which requires start and stop        times for every shop order at every process center. Moreover, it        is much easier to sequence than to schedule. In an exemplary        embodiment each flow would operate on shop orders of a specified        size (the order quantity) and is sequenced according to a        designated start date (SD). The sequence would be maintained as        much as possible throughout the flow by requiring each process        to always start the shop order in queue with the earliest start        date.    -   5. A technique to track production against demand that is able        to compute meaningful indicators that would signal conditions        corresponding to late orders, a capacity shortfall, and an        overabundance of capacity.    -   6. A “Capacity Trigger” indicating that either additional        capacity is needed to prevent a decline in on-time delivery        performance or that capacity should be reduced to prevent low        productivity, high inventory, and increased cost.        Make-to-stock policies may be characterized by a re-order point        (ROP) and a re-order quantity (ROQ) while make-to-order policies        may be characterized by a planned lead time (PLT) and a lot        size. Those skilled in the art will realize that the lot size        for the make-to-order policy is essentially equivalent to the        ROQ for the make-to-stock policy. These policies will henceforth        be referred to as ROP, ROQ, PLT policies.

These techniques and procedures are used to (1) execute to an optimalplan so long as the assumptions for the plan are suitably accurate and(2) to detect conditions when the assumptions are no longer suitablyaccurate to warrant continuation in the plan.

The invention also provides a system and a computer program implementingthe optimal execution processes and procedures.

FIG. 6 is a functional flow diagram incorporating principles of theinvention, showing detail of single Flow and single Stock that make up alarger supply chain. The flow sequence of FIG. 6 may be used inconjunction with a supply chain, such as shown in FIG. 1. Make-to-order(MTO) demand 101 arrives from customers and is converted into shoporders and maintained in a Virtual Queue 102 until released into theFlow by the CONWIP release mechanism 103.

The CONWIP release mechanism allows new shop orders into the Flowwhenever the Active work-in-process (WIP) level 109 falls below aspecified level 105. Other embodiments might convert the Active WIPlevel 109 to some sort of standard units and maintain a CONWIP levelaccordingly. Shop orders may be processed in the flow at individualprocess centers 108 a-All of the WIP between the release point and thestock is called Active WIP 109. Make-to-stock demand 111 is satisfieddirectly from Stock 107 and is managed using an Inventory Policy 106(e.g., a ROQ, ROP policy). In this exemplary embodiment, an order for Qparts is placed into the Virtual Queue whenever the inventory positionreaches the re-order point, r 104. The Planned Lead Time 110 includestime in the Virtual Queue, in Active WIP and the planned time spent inStock.

FIG. 7 is a block diagram illustrating an exemplary dynamic risk basedscheduling (DRS) system in which the functionality of the invention mayoperate, generally denoted by reference numeral 150. The functionalityprovided by the invention may operate with or be embodied in othersystems as well; FIG. 7 is just one exemplary version. The DynamicRisk-based Scheduling (DRS) system 151 supplies the functionalityaccording to the principles of the invention and may be implemented asone or more respective software modules operating on a suitablecomputer. The suitable computer typically comprises a processing unit, asystem memory which might include both temporary random access memoryand more permanent storage such as a disk drive, and a system bus thatcouples the processing unit to the various components of the computer.This computer is shown functioning as a server 152, but this is not arequirement.

Server 152 typically hosts three applications or “layers.” These are (1)the data layer comprising database components 160 to access the database 162, (2) the logic layer 158 comprising a high level language suchas C, C++, or Visual Basic to implement the optimal Planning andExecution algorithms described more below, and (3) the web interfacelayer 156 comprising software components that allow the overall DynamicRisk-based Scheduling functions to be accessed via a network 166. Thenetwork 166 could be a local intranet, wide-area network, or Internet.The connectivity may be accomplished by many different techniquesincluding wired or wireless techniques commonly known in the art.

An exemplary embodiment of the invention may include XML and WebServices 164 to provide direct access by the DRS system 151 to datastored in the ERP system 170 and/or the Manufacturing Execution System(MES) 172 via an application programming interface over the network 167.(Networks 166 and 167 could also be a common network). A planner (e.g.,a person using the DRS system) accesses the DRS system 151 via agraphical user interface (GUI) 168 operating over the network 166. Theplanner typically uses the same GUI 168 to implement the dynamic policygenerated by the DRS in the ERP system 170. The ERP system 170 typicallycommunicates with the MES 172 to provide direct controls to themanufacturing facility 174.

FIG. 8 is a block diagram illustrating the relationship of DRSoperations in conjunction with an existing MES and ERP system, inaccordance with principles of the invention. The DRS comprises two logicmodules, one for optimal Planning 120 and the other for optimalExecution 148. In this exemplary embodiment, the Planning Module 120receives demand, capacity, cost, and other data, 130, from the ERP/MESsystem 135 (typically from ERP) and returns optimal parameters ofcapacity, including any of ROP's, ROQ's, and PLT's, 125, to the ERP/MESsystem 135 (typically to the ERP). The ERP/MES system 135 provides arelease pool of shop orders (i.e., information of one or more shoporders) while the MES provides shop status and WIP location information140 to the DRS Execution Module 148. The DRS Execution Module 148provides a release signal based on the CONWIP protocol (and/or includingbased on the optimal parameters), and a trigger signal 145 to the MES.

FIG. 9 is a block diagram of a DRS based system that is similar to FIG.8 and which shows several advantages over existing supply chainmanagement systems, according to principles of the invention. The APOmodule of prior art systems (such as APO 52 of FIG. 2) is nowreplaceable with the optimal Planning Module 202 that includesalgorithms to optimize parameters used in the planning system 201including but not limited to capacity, ROP's, ROQs, and PLT's. Theseupdated parameters are then stored in the data bases 218. The PlanningModule 202 also provides the dynamic policy parameters including but notlimited to CONWIP levels for the Execution Module 212. In contrast tothe embodiment of FIG. 8 where the DRS comprises a separate ExecutionModule 148, the execution features of the DRS are now integrated into anexisting Execution System 212.

With the Planning Module 202, the planner is now enabled to perform aperiodic (e.g., monthly) optimization 203 that feeds the results intowhat becomes an improved planning and execution system 201/204. Thiseliminates any need to perform a detailed schedule by replacing such adetailed schedule with a dynamic policy operating along with the ERP/MESframework and within a CONWIP generalized pull production environment.The dynamic policy comprises a set of optimized ERP parameters thatoperate with traditional MRP (i.e., time-phased re-order points) togenerate both make-to-order and make-to-stock demands for all levels inthe bill of material. As a result, one difference between traditionalMRP and the new principles provided by the DRS system is that the shoporders are not released into production via a schedule (per traditionalMRP), but rather, are now pulled in according to the CONWIP protocol,according to the principles of the invention. This prevents theinevitable “WIP explosions” that are experienced by most MRP systemswhile maintaining the ERP planning and execution hierarchy.

The Execution Module 212 may be utilized via the GUI 168. Although theExecution Module 212 functions as though it were embodied in both theERP System and the MES (as is depicted here), it may be a logicalcomponent of the DRS 151 itself and typically resides on the DRS server152. Thus the ERP system 201 differs from the original ERP system 50 inthat the original Master Production Scheduling application 74 has beenreplaced by an Improved MPS that is provided by the Execution Module212. The enhanced MES 204 has replaced the traditional WIP tracking andDispatching components, such as FIG. 2, MES 54, with a CONWIP Releasefunction, a Demand to Production Tracking function, and a CapacityTrigger function that are supplied as part of the Execution Module 212.The planner may use the GUI 158, described more below, to interact withboth the Planning Module and the Execution Module in order to setparameters for these functions, to review the output, and, finally, toimplement the dynamic policy.

Inputs to the enhanced MES functions come from sensors and scanners 216on the shop floor or from direct data entry. Outputs go to shop floormonitors 215 or may be printed out for manual distribution. Theadvantages of the system and methods of the invention include periodicoptimization of the parameters used for planning 203 and real-timeexecution of a dynamic schedule 205, as opposed to periodic regenerationof a fixed schedule commonly used by prior art systems.

FIG. 10 is a flow diagram of an embodiment of a system involving an MESand ERP system, according to principles of the invention, generallydenoted by reference numeral 250. The process steps of Demand Forecast255, Aggregate Production Planning 260, and Capacity Resource Planning265 features remain as part of the overall process, as traditionallyknown. However, an optimal DRS Planning Module 270, functioningaccording to principles of the invention explained in more detail is nowalso used during the overall planning and execution process. Thisgreatly enhances the ability to balance the need for on-time delivery,minimal inventory, and high utilization of equipment and labor. Outputfrom the DRS Planning Module 270 (designated by dashed flow lines) isused by the MRP system 280 (ROQs, ROP's, PLT's), the CONWIP Releasemodule 295 (CONWIP levels) and by the Capacity Trigger 300 (e.g.,maximum probability of shortage). In traditional ERP, MTO demand and MTSforecasts 275 typically go into the MPS module (e.g., 74 of FIG. 3). Inthe case of a DRS enhanced ERP system, these demands go directly intothe gross requirements of the MRP module 280 and may be re-sequencedusing the Demand/Production Tracking module 305. This eliminates a greatdeal of manual rescheduling while the functionality of the MES is movedto the Execution Module 290, particularly by the Demand/ProductionTracking Module 305 that has much greater ability to model stochasticevents. The MRP module 280 uses MTO demand and MTS forecast along withinventory data 282 to generate a set of planned orders. Purchase ordersare released to suppliers on their planned start date. However, shoporders are released to the floor according to the CONWIP Releasefunctions 295. The progress of shop orders is tracked using theDemand/Production Tracking module 305. If multiple shop orders appearlikely to miss due dates, the Capacity Trigger 300 issues a TriggerSignal.

FIG. 11 is a flow diagram of an embodiment of DRS used for planning andexecution independently of an ERP system, according to principles of theinvention. FIG. 11, and all other flow diagrams and steps herein, mayequally represent a high-level block diagram of components of theinvention implementing the steps thereof. The steps of FIG. 11 (andother flow diagrams herein) may be implemented on computer program codein combination with the appropriate hardware having a processor(s) forexecution of the computer program code. This computer program code maybe stored on storage media such as a diskette, hard disk, CD-ROM,DVD-ROM or tape, as well as a memory storage device or collection ofmemory storage devices such as read-only memory (ROM) or random accessmemory (RAM). Additionally, the computer program code can be transferredto a workstation over the Internet or some other type of network,perhaps embedded in a carrier wave to be extracted for execution. Thesteps of the flow diagrams herein may be implemented on the systems ofFIGS. 7 and/or 9, for example, or other systems known in the art,

Continuing now with FIG. 11 at step 355, before (or at the start of)each planning period (e.g., monthly or quarterly), the dynamic policymay be optimized, step 360. This optimization includes but is notlimited to setting capacity levels for machines and labor, ROP's, ROQ's,PLT's for parts, and CONWIP levels for flows. After acquiring a good setof dynamic policy parameter(s), the system executes autonomously usingthe Dynamic Policy, step 280, and CONWIP Release, step 290, until either(1) the end of the planning period is reached or (2) the occurrence of acapacity trigger. If capacity is short, a signal to add capacity isgenerated, step 380. If demand is less than available capacity for along enough time, the Virtual Queue 102 will either empty or become verylow. At step 385, either of these conditions (empty or very low VirtualQueue) is an indicator that capacity is “over” 385, and a signal (i.e.,an electronically generated signal) to reduce capacity may be generated.

Capacity can be added in many ways including but not limited to workingovertime, adding a shift, working on a weekend day, or increasing headcount. Capacity can be reduced by reversing these processes as ineliminating overtime, taking away a shift, ending work on weekends, anddecreasing headcount. The DRS processes and procedures seek to providethe right amount of capacity for the realized demand without excess cost(e.g., overtime rates) while maintaining on-time delivery and minimalinventories. If capacity does not need to be adjusted the processcontinues 390 until the end of the period.

FIGS. 12A and 12B are flow diagrams of an embodiment of the DynamicPolicy and CONWIP, according to principles of the invention. The DynamicPolicy is similar to classic MRP and begins with the loading of therealized independent (i.e., outside) demand for all make-to-order itemsand an independent demand forecast for all make-to-stock items 510 (bothare hereinafter referred to as “demand”). At step 510, independentdemand orders and/or forecast are loaded. At step 520, these demands arenetted against available inventory and any pre-existing orders. At step530, the netted demands are then divided and/or collected into orders(both shop and purchase) using the optimized order quantities (ROQ). Atstep 540, a Start Date (SD) is computed for all items by subtracting thePlanned Lead Time (PLT) from the Due Date (DD) of the order. At step550, the combination of the sku, SD, and ROQ may be used with the Billof Material (BOM) to generate demand for component parts. At step 560, acheck is made whether there are more parts in the given Low Level Code.If so, then the process continues at step 520.

The entire logic is repeated until no more Levels are present step 570.The output is typically a collection of one or more purchase ordersand/or one or more shop orders. The purchase orders may be sent to thesuppliers on their SD.

Shop orders whose start date (SD) is before “today” go into the virtualqueue (VQ) 615. These shop orders are released into the flow using theCONWIP technique in which the process considers all flows in themanufacturing facility 610. At step 620, a check is made to see if theWIP in a given flow is below the established CONWIP. If so, at step 630the next shop order in the Virtual Queue may be released. Shop orders inthe Virtual Queue are typically arranged in earliest start-date order.This is repeated for all flows, step 640.

FIG. 13 is a flow diagram of an embodiment of the Demand/ProductionTracking (DPT) module of FIG. 10, according to principles of theinvention. The DPT module provides a graphical means to determinewhether the product flow is ahead of demand, behind demand, or issynchronized with demand. The exemplary process begins at step 710 byconsidering all of the orders in the VQ. At step 720, for each order, astatistical distribution of the finish time is estimated either byMonte-Carlo simulation or by using a stochastic model. The orders may beprioritized by start date and may utilize a plurality of routings. Thoseskilled in the art should understand and be able to make multipletransient Monte-Carlo simulations, each using a different random numberseed, and each starting with the current configuration to provide astatistical sample of finish times. This sample of times can be used toestimate a sample distribution using any of a number of statisticaltechniques. An exemplary technique includes estimating the cumulativedistribution probability for the i^(th) “order statistic” from a sampleof size n given by,

${F\left( t_{i} \right)} = \frac{i}{n + 1}$

At step 730, an estimation of the next associated demand time may bedetermined. The different orders are associated with the demands in theorder of their sequence as determined by their start date. Normally, theorder with the earliest SD is associated with the first demand instance,and so on. If demand instances are not of the same size as the orders,care must be taken to associate each demand instance with the properorder. Typically, demand associated with MTO has a degeneratedistribution associated with the time of its demand in that all theprobability is assigned to a single point in time. In either case, atstep 740, computation of the probability of shortage (i.e., late) may becomputed. At step 750, the expected amount of inventory (i.e.,inventory-days) that would accumulate before the demand date may becomputed. At step 760, a check is made whether there are more orders. Ifso, the process continues at step 720. If, however, there are no moreorders, the process continues at step 770, where with this information,an “overall probability of shortage” (OPS) maybe computed. At step 780,a total expected inventory-days (TEID) may be computed. One measure (ofmany) of OPS may be the expected number of items to be delivered on timedivided by the total demand. Another exemplary measure may be theexpected number of orders delivered entirely on time divided by thetotal number of orders. Other measures may be used as deemed suitable.At step 790, if the OPS measure is greater than a specified Trigger, aTrigger Signal indicating insufficient capacity may be issued. At step800, if the TEID is greater than a different specified Trigger, a Signalindicating a possible overabundance of capacity may be issued.

The Capacity Trigger typically works in two ways. One signal is thatthere is insufficient capacity and so more is needed. Exemplarytechniques to add more capacity include but are not limited to addingovertime, adding an extra shift (or hours), or adding more people to thelabor force. For supply chains operating all available machines 24 hoursper day, 7 days per week, no additional capacity is available and so theCapacity Trigger is an indication to reduce the amount of demand that isaccepted by the facility. The other way the Capacity Trigger works is toindicate when there is an overabundance of capacity. In this case, thereis more capacity than needed to meet demand and so the utilization ofthe machines and labor will be lower than desired. Since the cost oflabor and machines is now distributed over fewer parts, unit costs rise.Consequently, the Capacity Trigger indicates the need to reduce capacity(at least labor, usually) in order to reduce costs.

In other embodiments, as relating to step 790, the probability of lateshop orders may be computed continuously. Whenever the probabilityexceeds a set level, additional capacity is needed and a signal isgenerated. Other, somewhat simpler embodiments may also be employed suchas whenever the amount of work in the Virtual Queue exceeds a givenlevel, a signal for more capacity is generated.

Note that the way work is generated for the Virtual Queue, both by thereceipt of an outside order (such as 101, FIG. 6) and via consumption ofstock and the employment of an inventory policy (such as 106, FIG. 6),there is a limit to how far the flow can progress ahead of demand. Ifthere are no new outside orders and if all the stocks are above theirre-order points, there will be no demand in the Virtual Queue. Thus, thesimplest indicator of an overabundance of capacity is a Virtual Queuethat is either empty, or has very little work. The computation of TotalExpected Inventory Days provides additional information indicating howmuch extra inventory might be caused by orders finishing early.

FIG. 14 is a flow diagram describing an embodiment of the OptimizationModule, according to principles of the invention. At step 405, theOptimization begins with a smoothing of demand over the long-term. Inalternate embodiments, such smoothing could be part of another module inthe ERP system such as the Aggregate Production Planning module.Nonetheless, the decision is made whether to employ a “chase” strategyby adding and subtracting capacity for peaks and valleys in demand, orwhether to smooth demand by “pulling in” demand “spikes” from the futureand by “pushing out” high demand early on. A chase strategy is typicallymore costly from a capacity view because of numerous capacity changes.On the other hand, pulling in demand creates additional inventory whilepushing out high demand may result in late shop orders. Nonetheless, atstep 410, because a dynamic policy can be established now with staticparameters, it is possible to establish a relatively constant level ofcapacity for the operation. This level might be adjusted during theoptimization procedure but it typically remains static for the planningperiod. This is typically not a problem since most production facilitiesadjust basic capacity relatively rarely (e.g., once per month, or someother time period).

At step 415, the optimal ROQs and ROP's for the given capacity levels(both machine and labor) may be computed. In some modes of theoptimization, the objective may include minimizing the sum of the WIPand finished stock inventory carrying cost plus any out of pocket costssubject to constraints on capacity, percent on-time delivery, andparticular constraints on the ROQs (e.g., minimum, maximum, and ROQincrements).

At step 420, an incidental output of process is the “LaGrangemultipliers” for the capacity constraints. These numbers are useful inthat they represent the amount of reduction in the total cost of theobjective (i.e., the total of WIP and stock carrying costs plusout-of-pocket costs) per unit of additional capacity (e.g., one extrahour of time available on a machine or for a worker). If this number islarge compared to the cost of said capacity, then one should increasethe capacity. However, if there is plenty of capacity, then thesenumbers will be zero indicating that capacity can be reduced. At step425, the capacity should be adjusted until the LaGrange multipliers arereasonable compared to the cost of additional capacity. Once this isachieved, at step 430, the values of the ROQs and re-order points can beapplied to the dynamic policy.

FIG. 15 is an equation showing the relation between demand (D), OOP cost(V), setup time (S), item cost (c), inventory carrying cost ratio (h)and ROQ (Q) and the LaGrange multipliers (λ), according to principles ofthe invention. The equation may be employed to determine an initial ROQfor each item in the data base. This initial ROQ may be modified byadditional constraints such as minimum ROQ, maximum ROQ, and an ROQincrement. The ROQ is determined for every part (subscript i) anddepends on parameters of the part itself as well as parameters of eachresource (subscript k) which depend on parameters for each operation atthe resource (subscript j). The initial ROQ is also influenced by thequantity, α, which depends on the part and the resource. The resourcedependency is a function of setup time and the fraction of demand thatvisits the operation at the given resource. Note that δ is equal to zeroif the part does not visit the operation and therefore there is nocontribution to α. These terms are summed to generate a value for a foreach part-resource pair. α represents the setup time required for agiven part at a given resource. The LaGrange multiplier, λ, becomes thelink between the setup of the item and the resource capacity. Theprocess by which this dependency is determined is given in the flowdiagram of FIG. 16, described in more detail below. The value of λ isthe amount that the total of the OOP cost and the WIP and inventorycarrying cost can be reduced by increasing the capacity of the resourcein question by one unit. For instance, if λ is equal to $200 and theunit of capacity is one hour then one will be able to reduce the cost ofthe production plan by adding an additional hour so long as thatadditional hour cost less than $200. (This decision is made as part ofstep 425 of FIG. 14, for example).

Those skilled in the art will know that a necessary condition for aproduction plan to be optimal is that λ must be zero for any resourcewith abundant capacity and that there will be no extra (slack) capacityfor any resource for which λ is greater than zero. This notion isapplied in FIG. 16. FIG. 16 is a flow diagram showing steps of anembodiment that may be used to determine an initial set of optimalre-order quantities, according to principles of the invention. Such aninitial set may be subject to the aforementioned constraints on maximum,minimum and ROQ increment as well as other practical considerations.Moreover, it is likely that this set of ROQ values can be improved uponby applying a global search technique.

Continuing now with step 1010, data for demand and capacity from the ERPsystem are loaded. Such data may be stored in an ERP database (e.g.,database 218) and may be obtained using a network (e.g., network 167)using an application programming interface. At step 1020, the LaGrangemultipliers, λ, are first all set to zero. At step 1020, the ROQ valuesare computed and then adjusted according to ROQ size constraints (i.e.,minimum, maximum, increment). At step 1030, using these computed ROQvalues, the capacity slack values (available capacity minus capacityused by the plan) are computed for each resource. Those skilled in theart should realize that if the production plan resulting from all λvalues set to zero is feasible (i.e., it does not violate capacityconstraints), then the plan is also optimal. At step 1040, thefeasibility of the solution is checked by considering all the slackvalues (if all are positive, then the solution is feasible). If thesolution is not feasible, at step 1050, the associated value of λ shouldbe increased. However, the solution may be “super-feasible” meaning thatthere is more than enough capacity everywhere and the cost of the plancan be reduced while remaining feasible. At step 1060, a check is madeif the solution is super-feasible. An indication of this is having slackcapacity when the associated λ is positive. If this is the case, at step1070, the value of the associated λ is reduced. Such iterations continueuntil there are practically no infeasibilities as well as nosuper-feasibilities. Those skilled in the art will understand thesignificance of the term “practically” because it is virtuallyimpossible to determine a set of λ values that result in the slackvalues of tight resources that are exactly zero. Consequently, theprocess concludes when there are no infeasible constraints and when thesuper-feasibilities are not significant. An example of such a checkwould be whenever the slack is less than one percent of that available.Alternatively, the user might deem that there are no infeasibleconstraints and the super-feasibilities are not significant.

Those skilled in the art will also realize the need for the correctionto the λ values to become smaller with each iteration in order to forceconvergence. This can be easily accomplished reducing the amount bywhich the λ values are adjusted with each iteration.

Once the feasibility and super-feasibility conditions are satisfied, atstep 1080, a global search technique to improve on the ROQ's and todetermine an optimal set of ROP's or PLT's is performed. Typical globalsearch techniques include the “downhill simplex” technique of Nelder andMeade as well as conjugate direction methods. The global searchtechnique would employ stochastic queueing and inventory models todetermine an “objective function” that includes performance measuressuch as out-of-pocket costs, raw material, WIP, and finished goodsinventory levels and also customer service levels. Several variations ofthe global objective exist and may include, in addition to theout-of-pocket costs and finished goods inventory carrying cost, WIP andraw material inventory carrying costs and as well as a cost ofbackorders. A different approach might include performing the globalsearch only on the ROQ values and would subsequently determine a set ofROP's (or PLT's) that achieved a desired customer service level. Bothapproaches do not require constraints on capacity because (1) theinitial solution is feasible and (2) the WIP grows prohibitively largewhen approaching the capacity limit. Thus, an unconstrained globalsearch will likely result in an optimal set of ROP/PLT values and ROQvalues.

FIG. 17 is a representation of an exemplary graphical user interface(GUI) of the invention providing output and through which a user mayinput policy parameters and interact with the optimal Planning Module,generally denoted by reference numeral 1100. The current policy (CurrentROQ/Current ROP) 1105 is displayed along with the resulting performance1150 for each part (i.e., each “Item ID” such as Part1, Part10-Part19)that includes on-hand inventory, fill rate (percentage on-time), averagecycle time, planned lead time, WIP, and inventory carrying cost. Alsodisplayed are the total inventory carrying cost 1110, the totalout-of-pocket cost 1120, and their sum 1130 which in this case is$11,382 (circled).

FIG. 18 is a representation of an exemplary graphical user interface(GUI) of the invention providing output showing the results after theoptimization, generally denoted by reference numeral 1200. The optimizedpolicy (Current ROP/Current ROQ) 1205 is displayed along with theresulting performance for each part regarding inventory carrying cost,cycle time, out-of-pocket cost and on-time delivery 1250. The totalinventory carrying cost 1210 and the total OOP cost 1220 is alsodisplayed. The sum of these 1230 is also indicated which, in this case,is $5,753 (circled) indicating a significant savings over the previouspolicy. Two buttons on the screen allow the user to present the valuesof the LaGrange multipliers for both machine capacity (button 1260) andlabor capacity (button 1270).

FIG. 19 is a representation of an exemplary graphical user interface(GUI) providing output showing the LaGrange multipliers for machinecapacity, according to principles of the invention, generally denoted byreference numeral 1300. In this exemplary embodiment, results aredisplayed for each process center 1310 (i.e., column denoted by “ProcessCenter ID”) that include entries showing how much time is available(hrs/period), how much “Time Used” by the plan (hrs/period), the “MaxAllowed Utilization” (%), and the resulting “Utilization” (%). The GUIalso indicates the slack under the column titled, “Available TimeRemaining” 1320, as well as the value of the LaGrange multiplier itselfunder the column titled, “Cost Decrease per Extra Hour Available” 1330.In this example only one process center has a positive LaGrangemultiplier indicating that $41 could be saved from out-of-pocket costsand inventory carrying costs for every additional hour devoted to “PC1.”

FIG. 20 is a flow diagram of steps of an embodiment used in the Planningmodule to determine optimal CONWIP levels for a flow, according toprinciples of the invention. As shown in this embodiment, a graphicaloutput of cycle time (CT) and throughput (TH) for a plurality of WIPlevels is provided for a single flow. This process improves the inherentintangibles concerning tradeoffs between longer cycle time and higherutilization of resources. Thus, instead of requiring the planner tospecify a set of relative costs for cycle time and equipmentutilization, this embodiment provides a broad set of alternatives tochoose from (i.e., the various WIP levels).

The procedure is repeated for every WIP level desired, step 910. For agiven WIP level, an estimation of the corresponding cycle time (CT) andthroughput (TH) using either a Monte-Carlo simulation model or anapproximate closed queueing network is calculated. In some embodiments,whenever an order is completed, a new one is pulled into the flow,thereby maintaining a constant WIP level with regard to orders. Otherembodiments might consider the WIP in pieces while another may considerWIP in some common unit of measure (e.g., kilograms). If the systemcontains more than one type of product, new products are pulled inaccording to the probability of their occurrence in demand. Once the THand CT are estimated, the values are typically stored and plotted, suchas on the graphical user interface 930. This is repeated for each WIPlevel desired, step 940.

FIG. 21 is a graph showing the output of an embodiment of the optimalCONWIP level estimation tool, according to principles of the invention,generally denoted by reference numeral 1400. The GUI 1400 shows outputfor two plots of TH, one for the ideal case (solid line) 1420 and theother for what the flow is capable of (triangles) 1430. The GUIcontrasts these output levels with the average overall demand(horizontal line) 1410. The GUI also contains output showing two plotsof cycle time, one for the ideal case (solid line) 1440 and another forthe flow in question (diamonds) 1450. Two vertical lines indicate,respectively, the minimum WIP required (around 37) 1460 and arecommended WIP (around 52) 1470. The minimum WIP indicates how much WIPis required to just meet demand on average. The recommended indicatedhow much WIP is required to meet demand more reliably. The decision isdifficult because the more reliable WIP level requires cycle times thatare approximately 25% longer.

FIG. 22 is a representation of a graphical user interface (GUI) of theinvention showing the output of an embodiment of the CONWIP Sequenceexecution process, generally denoted by reference numeral 1500. Outputincludes general information 1510 such as schedule start and end date,planned production rate, etc., as well as the CONWIP limit 1520.Particular information for individual shop orders is also included inthe output including the order of the work sequence 1530, the due dates1540, early, late, and expected completion dates 1550, the due datestatus (i.e., early, late, on-time) 1560, and out indicating the statusof the shop order 1570. In this exemplary embodiment, the statusindicates whether the shop order is currently active (in WIP),completed, or should not be started (Wait).

FIG. 23A is a representation of a graphical user interface (GUI) of theinvention showing the output of an embodiment of the Production/DemandTracking with a Capacity Trigger, generally denoted by reference numeral1610. FIG. 23A shows output for on-time delivery and inventory. FIG. 23Bis a pie chart output showing how much overtime is used, in accordancewith FIG. 23A, generally denoted by reference numeral 1620.

Referring now to FIG. 24A, the vertical bars 1630 denote the totalexpected inventory-days (TEID) while the solid diamonds 1640 denoteoverall probability of shortage (OPS). The solid line 1650 is outputshowing the Capacity Trigger. If any OPS point exceeds the CapacityTrigger, additional capacity should be considered. FIG. 24B may beconsidered an overtime graph and provides output in the form of a piechart 1620 indicating that no overtime is being used 1660.

FIG. 24A is a representation of an exemplary graphical user interface(GUI) of the invention showing the output of an embodiment of theProduction/Demand Tracking with a Capacity Trigger, generally denoted by1710. FIG. 24B is a pie chart reflecting overtime usage in accordancewith the output of FIG. 24A. FIG. 24A differs from FIG. 23A in thatovertime is being used.

FIG. 24B is a pie chart reflecting overtime usage corresponding to theoutput of FIG. 24A and according to principles of the invention. Piechart 1720 shows that about one third of the “pie” as indicating thatone third of the available overtime is being used 1760. The chart 1710is output that shows the predicted total expected inventory-days 1730and the overall probability of shortage 1740 along with the CapacityTrigger 1750. In the case of FIG. 24A, because the production rate isgreater while demand has remained constant, the TEID 1730 is higher thenthan shown in FIG. 23A, 1630, while the OPS 1740 is lower than 1640.Note that the OPS exceeds the Capacity Trigger on seven days when noovertime is used as in FIG. 23A; but never exceeds it when the overtimeis used, as in FIG. 24A.

Various modifications and variations of the described methods andsystems of the invention will be apparent to those skilled in the artwithout departing from the scope and spirit of the invention. Althoughthe invention has been described in connection with specific preferredembodiments, it should be understood that the invention as claimedshould not be unduly limited to such specific embodiments. Indeed,various modifications of the described modes for carrying out theinvention which are obvious to those skilled in the art are intended tobe within the scope of the following claims.

1-32. (canceled)
 33. A computer implemented method for trackingproduction in a given CONWIP product flow against demand associated witha plurality of orders in the product flow said method comprising thesteps of: (i) determining when the Virtual Queue has an overabundance ofshop orders for a product flow thereby generating a first electronicsignal indicating a need for more capacity; (ii) detecting when theVirtual Queue has an insufficient number of shop orders in the productflow thereby generating a second electronic signal indicating acondition of over capacity; (iii) determining overall probability ofshortage for a set of associated demands for the product flow; (iv)determining expected inventory-days for each of the plurality of ordersin the product flow; and (v) displaying output showing one of theprobability of shortage and total expected inventory-days versus aspecified parameter for managing production inventory, wherein each ofthe steps (i) to (v) are performed by a computer.
 34. Thecomputer-implemented method of claim 33, further comprising the step ofdetecting a condition of insufficient capacity and generating a thirdelectronic signal indicative of the insufficient capacity.
 35. Thecomputer-implemented method of claim 33, further comprising the step ofdetecting a condition of an overabundance of capacity and generating afourth electronic signal indicative of the overabundance of capacity.36. The computer-implemented method of claim 33, further comprising: i)determining a probability distribution of finish times for all orders inthe flow; ii) determining a probability distribution of associateddemand time for at least one of the plurality of orders in the flow;iii) determining the probability of shortage for the at least oneassociated demand based at least in part on both probabilitydistributions; and displaying an output showing the overall probabilityof shortage for the at least one associated demand versus a specifiedparameter.